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On the Sharpness of the Estimate in a Theorem Concerning the Half Smoothness of a Function Holomorphic in a Ball
Let B n be the unit ball and S n be the unit sphere in C n , n ≥ 2. Let 0 < α < 1, and define a function f on as follows: The main result of the paper is the following theorem: the function ζ ↦ | f (ζ)| on the unit sphere S n belongs to the Hölder class H α ( S n ), while the function f does n...
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| Published in: | Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-03, Vol.243 (6), p.985-992 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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| container_end_page | 992 |
| container_issue | 6 |
| container_start_page | 985 |
| container_title | Journal of mathematical sciences (New York, N.Y.) |
| container_volume | 243 |
| creator | Shirokov, N. A. |
| description | Let B
n
be the unit ball and
S
n
be the unit sphere in C
n
,
n
≥ 2. Let 0 <
α
< 1, and define a function
f
on
as follows:
The main result of the paper is the following theorem: the function ζ ↦ |
f
(ζ)| on the unit sphere
S
n
belongs to the Hölder class
H
α
(
S
n
), while the function f does not belong to the Hölder class
for any
ε >
0
. |
| doi_str_mv | 10.1007/s10958-019-04599-x |
| format | article |
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n
be the unit ball and
S
n
be the unit sphere in C
n
,
n
≥ 2. Let 0 <
α
< 1, and define a function
f
on
as follows:
The main result of the paper is the following theorem: the function ζ ↦ |
f
(ζ)| on the unit sphere
S
n
belongs to the Hölder class
H
α
(
S
n
), while the function f does not belong to the Hölder class
for any
ε >
0
.</description><identifier>ISSN: 1072-3374</identifier><identifier>EISSN: 1573-8795</identifier><identifier>DOI: 10.1007/s10958-019-04599-x</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Mathematics ; Mathematics and Statistics ; Sharpness ; Smoothness ; Theorems</subject><ispartof>Journal of mathematical sciences (New York, N.Y.), 2020-03, Vol.243 (6), p.985-992</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2019</rights><rights>COPYRIGHT 2019 Springer</rights><rights>COPYRIGHT 2020 Springer</rights><rights>2019© Springer Science+Business Media, LLC, part of Springer Nature 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c463x-20e58360a2760faea9d6624bdbcc3b22c2bb3d32f3f48842c3050bfbcf0086ae3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Shirokov, N. A.</creatorcontrib><title>On the Sharpness of the Estimate in a Theorem Concerning the Half Smoothness of a Function Holomorphic in a Ball</title><title>Journal of mathematical sciences (New York, N.Y.)</title><addtitle>J Math Sci</addtitle><description>Let B
n
be the unit ball and
S
n
be the unit sphere in C
n
,
n
≥ 2. Let 0 <
α
< 1, and define a function
f
on
as follows:
The main result of the paper is the following theorem: the function ζ ↦ |
f
(ζ)| on the unit sphere
S
n
belongs to the Hölder class
H
α
(
S
n
), while the function f does not belong to the Hölder class
for any
ε >
0
.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Sharpness</subject><subject>Smoothness</subject><subject>Theorems</subject><issn>1072-3374</issn><issn>1573-8795</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNqNkk9r2zAYh81YYV23L7CTYKcd3OqPJdvHLrRLoVBY2rOQlVe2iy15kgLZt58WtzSB0BYdJMTz_F6Qfln2jeBzgnF5EQiueZVjUue44HWdbz9kp4SXLK_Kmn9MZ1zSnLGy-JR9DuERJ0lU7DSb7iyKHaBVp_xkIQTkzO7iKsR-VBFQb5FC9x04DyNaOKvB2962O2ipBoNWo3Oxe3YVut5YHXtn0dINbnR-6no9p_xUw_AlOzFqCPD1aT_LHq6v7hfL_Pbu183i8jbXhWDbnGLgFRNY0VJgo0DVayFo0awbrVlDqaZNw9aMGmaKqiqoZpjjxjTaYFwJBews-z7nTt792UCI8tFtvE0jJWWkxIIKwV-oVg0ge2tc9EqPfdDyUlQ0PRJn5esU4UwQLEii8iNUCxa8GpwF06frg9R38Xv550f4tNYw9vrogPcJexN-HAiJibCNrdqEIG9Wvw_D32T3cunMau9C8GDk5FO5_F9JsPzfXzn3V6b-yl1_5TZJbJZCgm0L_uUDX7H-AUo_7Yg</recordid><startdate>20200323</startdate><enddate>20200323</enddate><creator>Shirokov, N. A.</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ISR</scope></search><sort><creationdate>20200323</creationdate><title>On the Sharpness of the Estimate in a Theorem Concerning the Half Smoothness of a Function Holomorphic in a Ball</title><author>Shirokov, N. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c463x-20e58360a2760faea9d6624bdbcc3b22c2bb3d32f3f48842c3050bfbcf0086ae3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Sharpness</topic><topic>Smoothness</topic><topic>Theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shirokov, N. A.</creatorcontrib><collection>CrossRef</collection><collection>Gale In Context: Science</collection><jtitle>Journal of mathematical sciences (New York, N.Y.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shirokov, N. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Sharpness of the Estimate in a Theorem Concerning the Half Smoothness of a Function Holomorphic in a Ball</atitle><jtitle>Journal of mathematical sciences (New York, N.Y.)</jtitle><stitle>J Math Sci</stitle><date>2020-03-23</date><risdate>2020</risdate><volume>243</volume><issue>6</issue><spage>985</spage><epage>992</epage><pages>985-992</pages><issn>1072-3374</issn><eissn>1573-8795</eissn><abstract>Let B
n
be the unit ball and
S
n
be the unit sphere in C
n
,
n
≥ 2. Let 0 <
α
< 1, and define a function
f
on
as follows:
The main result of the paper is the following theorem: the function ζ ↦ |
f
(ζ)| on the unit sphere
S
n
belongs to the Hölder class
H
α
(
S
n
), while the function f does not belong to the Hölder class
for any
ε >
0
.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10958-019-04599-x</doi><tpages>8</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1072-3374 |
| ispartof | Journal of mathematical sciences (New York, N.Y.), 2020-03, Vol.243 (6), p.985-992 |
| issn | 1072-3374 1573-8795 |
| language | eng |
| recordid | cdi_proquest_journals_2317062665 |
| source | Springer Nature |
| subjects | Mathematics Mathematics and Statistics Sharpness Smoothness Theorems |
| title | On the Sharpness of the Estimate in a Theorem Concerning the Half Smoothness of a Function Holomorphic in a Ball |
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